5L 2s/Muddles: Difference between revisions

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The term "'''diatonic scale'''" is an umbrella term that not only refers to the [[5L 2s]] [[MOS scale]], but also to a group of [[muddles]] and [[MODmuddles]] that are related to it.  This page is for the cataloguing of these muddles.  For the sake of ease, "L<sub>1</sub>" refers to the larger of two large step sizes while "L<sub>2</sub>" refers to the smaller of two large step sizes, and likewise "s<sub>1</sub>" refers to the larger of two small step sizes while "s<sub>2</sub>" refers to the smaller of two small step sizes.  For muddles where there's only a single size of large step, a simple "L" will be used, and likewise, for muddles where there's only a single size of small step, a simple "s" will be used.
{{breadcrumb}}
The term "'''diatonic scale'''" is an umbrella term that not only refers to the [[5L&nbsp;2s]] [[MOS scale]], but also to the group of [[muddle]]s and [[MODmuddle]]s that both resemble it and are related to it.  This page is for the cataloguing of these muddles.  For the sake of ease, "L<sub>1</sub>" refers to the larger of two large step sizes while "L<sub>2</sub>" refers to the smaller of two large step sizes, and likewise "s<sub>1</sub>" refers to the larger of two small step sizes while "s<sub>2</sub>" refers to the smaller of two small step sizes.  For muddles where there's only a single size of large step, a simple "L" will be used, and likewise, for muddles where there's only a single size of small step, a simple "s" will be used.


== 3L<sub>1</sub> 2L<sub>2</sub> 2s ==
== 3L<sub>1</sub> 2L<sub>2</sub> 2s ==
The '''3L<sub>1</sub> 2L<sub>2</sub> 2s''' muddle can be denoted as '''Ptolemaic-Auric Diatonic Scale''' on account of the 3L<sub>1</sub> 2L<sub>2</sub> 2s being the step-size combination being shared by both the well-known '''[[Zarlino|Ptolemaic Sequence]]''', and [[User:Aura|Aura]]'s preferred tuning of the Ionian scale, albeit the exact step patterns differ between the two scales.  By default, the Ptolemaic-Auric Diatonic Scale has the pattern of L<sub>1</sub>L<sub>2</sub>sL<sub>1</sub>L<sub>1</sub>L<sub>2</sub>s, which was chosen as the standard arrangement for representing this particular step-size combination both because it uses two identical tetrachords just like the Pythagorean Diatonic Scale to which it's related, and because of the benefits this arrangement offers in the [[5-limit]].
{{see also|Nicetone}}


The 5-limit version the Ptolemaic-Auric Diatonic Scale- the tuning preferred by Aura- may be referred to as the '''Dualharmonic Ionian Scale''' on account of every scale degree being a member of either the Tonic's [[harmonic series]] or [[subharmonic series]]. The Dualharmonic Ionian Scale actually seems to be the optimal form for the Ionian scale- which is often considered the default diatonic mode by non-microtonalists- in terms of harmonic construction.  This form can be considered optimal for a 5-limit Ionian scale because the [[27/20]] wolf fourth is placed between the third and sixth scale degrees, which has the effect of creating both a really strong VIm-IIm-VM-IM cadence and a really powerful deceptive cadence using the VIm chord, while the IVM chord is in some ways less likely to be accidentally tonicized on account of it having a more tense sound.
The {{nowrap|'''3L<sub>1</sub> 2L<sub>2</sub> 2s'''}} muddle can be denoted as the '''Ptolemaic diatonic scale''' or as '''[[Nicetone]]''' on account of the {{nowrap|3L<sub>1</sub> 2L<sub>2</sub> 2s}} being the step-size combination of the well-known '''[[Zarlino|Ptolemaic sequence]]'''. By default, the Ptolemaic diatonic scale has the pattern of L<sub>1</sub>L<sub>2</sub>sL<sub>1</sub>L<sub>2</sub>L<sub>1</sub>s, which was chosen as the standard arrangement for representing this particular step-size combination due to the Ptolemaic Sequence being a more evenly distributed [[MV3]] scale, though to be fair, it is a chiral scale that has the other variant of L<sub>2</sub>L<sub>1</sub>sL<sub>1</sub>L<sub>2</sub>L<sub>1</sub>s.


[[File:Study in Ionian.mp3|thumb|none|A study piece by Aura using the Dualharmonic Ionian Scale, which has the following intervals: [[1/1]] [[9/8]] [[5/4]] [[4/3]] [[3/2]] [[27/16]] [[15/8]] [[2/1]].]]
== 2L<sub>1</sub> 3L<sub>2</sub> 2s ==
{{see also|Interdia}}
 
Aside from the Ptolemaic diatonic scale, the {{nowrap|'''2L<sub>1</sub> 3L<sub>2</sub> 2s'''}} muddle, which can be denoted as '''[[Interdia]]''', is the one of the more frequently encountered 5L&nbsp;2s muddles.
 
== 5L 1s<sub>1</sub> 1s<sub>2</sub> ==
The following [[18edo]] irregular diatonics, which are derived by stacking alternating 667{{c}} and 733{{c}} fifths, belong to this category: {{dash|0, 200, 400, 533, 733, 933, 1133, 1200}} and {{dash|0, 200, 400, 467, 667, 867, 1067, 1200}}.


== 2L<sub>1</sub> 3L<sub>2</sub> 2s ==
[[Category:Diatonic]]
Aside from the Ptolemaic-Auric Diatonic Scale, the '''2L<sub>1</sub> 3L<sub>2</sub> 2s''' muddle is the one of the more frequently encountered 5L 2s muddles.
[[Category:MOS muddles]]

Latest revision as of 16:16, 8 March 2025

< 5L 2s

The term "diatonic scale" is an umbrella term that not only refers to the 5L 2s MOS scale, but also to the group of muddles and MODmuddles that both resemble it and are related to it. This page is for the cataloguing of these muddles. For the sake of ease, "L1" refers to the larger of two large step sizes while "L2" refers to the smaller of two large step sizes, and likewise "s1" refers to the larger of two small step sizes while "s2" refers to the smaller of two small step sizes. For muddles where there's only a single size of large step, a simple "L" will be used, and likewise, for muddles where there's only a single size of small step, a simple "s" will be used.

3L1 2L2 2s

See also: Nicetone

The 3L1 2L2 2s muddle can be denoted as the Ptolemaic diatonic scale or as Nicetone on account of the 3L1 2L2 2s being the step-size combination of the well-known Ptolemaic sequence. By default, the Ptolemaic diatonic scale has the pattern of L1L2sL1L2L1s, which was chosen as the standard arrangement for representing this particular step-size combination due to the Ptolemaic Sequence being a more evenly distributed MV3 scale, though to be fair, it is a chiral scale that has the other variant of L2L1sL1L2L1s.

2L1 3L2 2s

See also: Interdia

Aside from the Ptolemaic diatonic scale, the 2L1 3L2 2s muddle, which can be denoted as Interdia, is the one of the more frequently encountered 5L 2s muddles.

5L 1s1 1s2

The following 18edo irregular diatonics, which are derived by stacking alternating 667 ¢ and 733 ¢ fifths, belong to this category: 0 – 200 – 400 – 533 – 733 – 933 – 1133 – 1200 and 0 – 200 – 400 – 467 – 667 – 867 – 1067 – 1200.

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